Alligning vertices in a UV image
If those UVs are exactly the same, you can align UVs to some common vertex and then rotate one UV with enabled vertex snapping and snap the rotation to some vertex of the other UV.




Enable snapping Shift+Tab
Set Snap UV Element to Vertex Ctrl+Shift+Tab
Set Selection Mode to Island Ctrl+Tab
Grab one island G and align it to corresponding vertex of the other UV island
Change Selection Mode to Vertex, select the common vertex and hit Shift+S to set Cursor to Selected, so you can use this vertex as a pivot point in next step
Change Pivot to 2D Cursor .
This is quite unpredictable but hopefully it will work - rotate the UV R and hover your cursor over vertices on the second UV until the rotation snap to it.


If your UVs are not exactly the same, you can then select all vertices and press W > Remove Doubles to merge vertices close to each other.